They can be used for crafting Fire Resistance Potions in your Crafting Menu (opened with "q" as the default key) or at any Crafting Table in older worlds.
They can also be used as an ingredient in Basic Health Potions, Stone Mining Cells, Taming Collars, Golden Potions and Stamina Regeneration Potions. For all of these recipes you can choose from different possible flowers by clicking on the flower-icon with the two small golden arrows in the selected recipe in your crafting menu window.
Tundra flowers can be placed for decoration, for example into Flower Pots, Wood Planters or on Wall Shelves, but cannot be used well for building, as they do not have cubic shapes. They also don't glow in the night and might not help with spawning any creatures.